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Friday, July 23, 2010

Use formative latent variables with caution

One should use formative latent variables (LVs) with caution in structural equation modeling analyses using WarpPLS. It is not uncommon to see formative LVs being created simply by casually aggregating indicators, without much concern about the indicators being actually facets of the same construct. See this post for more details.

It is also important to stress that formative LVs are better assessed when included as part of a model. This is preferable to analyzing formative LVs individually; that is, as “models” that include one single LV. The loadings and cross-loadings table takes into consideration both formative and reflective LVs in its calculation, and may suggest that some indicators do not “belong” to a formative LV.

Also, certain model parameters may become unstable due to collinearity. High collinearity among indicators is to be expected in reflective LV measurement, but not in formative LV measurement. In the context of formative LV assessment, collinearity may be reflected in unstable weights, where unexpected P values (usually statistically non-significant) are associated with weights.

In formative LVs, indicators are expected to measure different facets of the LV, not the same thing. If two (or more) indicators are collinear in a formative LV, it may be a good idea to collapse them into one indicator. This can be done by defining second order LVs (a two-step, somewhat complex procedure), averaging the indicators, or simply eliminating one of the indicators from the analysis.

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